PER CURIAM.
Kory Ray Smith entered a conditional guilty plea to the charge of knowing possession of counterfeit currency, in violation of 18 U.S.C. §§ 2 and 472. He reserved the right to appeal the district court’s denial of his pre-trial motion to suppress evidence. Smith now argues that the district court erred in (1) reversing its initial grant of his motion to suppress, (2) denying the motion to suppress, and (3) applying an incorrect standard of review to adjust his sentence. We have jurisdiction pursuant to 28 U.S.C. § 1291, and we affirm the district court.
I. BACKGROUND
Kory Ray Smith was driving a Chevrolet Camaro at 96 miles per hour with the high beam lights on when he passed a California Highway Patrol (“CHP”) car moving in the opposite direction. CHP Officers Eric Price and Timothy Ratcliff pulled Smith over. When Officer Price approached the Camaro and requested Smith’s license and registration, Smith said that he did not have any identification with him. Smith stated that he was licensed to drive in the State of Arizona. Officer Price then asked Smith to get out of his car and walk over to the patrol car.
At the front of the patrol car, Officer Price asked Smith his name, date of birth, and home address. Smith responded that his name was Vernon Paul Smith, that he was born on January 27, 1971, and that he lived on Fox Street in Mesa, Arizona. Officer Price contacted CHP dispatch to determine whether the California or Arizona driver’s license databases included a license that matched this information. CHP dispatch reported that it found no match. Officer Price confronted Smith with this fact, but Smith maintained that the information he had provided was accurate. Officer Price then approached the passenger of the Camaro, Jaime Beth Cot-tle, and inquired as to the driver’s name. Cottle responded that she only knew his first name, which was Vernon, and that she had only known him for about a month.
Officer Price returned to the front of the patrol car and, with Officer Ratcliff at his [947]*947side, asked Smith whether he knew his social security number. Smith provided the officers with a social security number. Dispatch then reported that the social security number corresponded to Vernon Paul Smith of Mesa, Arizona, born January 27, 1970. Dispatch also informed the officers that Vernon Smith had brown hair and eyes, stood six feet tall, and weighed 200 pounds. Officers Price and Ratcliff observed that Smith had blue eyes, stood five feet eight inches, and weighed approximately 175 pounds. Officer Ratcliff informed Smith of this discrepancy, while Officer Price patted Smith down in search of a wallet. Finding no wallet, Officer Price again asked Smith to divulge his identity.
While Officer Price was questioning Smith about his identity, Officer Ratcliff returned to the Camaro and searched it for Smith’s identification. After a brief search of the car’s interior, Officer Ratcliff uncovered a black wallet wedged under the rear seat. The wallet contained a driver’s license and an identification card, each of which had Smith’s picture on them. The driver’s license was issued under the name Steven Stone, and was eventually discovered to be fake. The identification card was issued from the State of Arizona to Kory Ray Smith and was authentic.
While Officer Ratcliff searched the car, Officer Price continued to question Smith. Smith finally conceded that he had provided the officers with his brother’s identification information, and that his real name was Kory Ray Smith. Officer Price contacted dispatch with the new date of birth Smith had provided and confirmed that Smith was in fact Kory Ray Smith. Officer Price then arrested Smith for falsely impersonating another and placed him in the patrol car. Once Smith was in the patrol car, Officer Ratcliff returned from searching the Camaro and informed Officer Price that he had found Smith’s identification. Officer Price stated that Smith had already disclosed his identity.
Because the wallet contained currency, Officer Ratcliff asked Smith whether he wanted to leave the money in the wallet during booking or to leave it with Cottle. Smith told Officer Ratcliff to give the money to Cottle. When Officer Ratcliff took the money out of the wallet he discovered that the bills had neither the texture nor the appearance of real money. After comparing the bills in Smith’s wallet to bills in their own, the officers concluded that the currency in the wallet was counterfeit. Officer Ratcliff then returned to the Cama-ro and examined a $20 bill that he had previously noticed on the floor, which also appeared to be counterfeit.
On July 2, 2003, a federal grand jury indicted Smith for knowing possession of falsely made, forged and counterfeited obligations and securities of the United States, in violation of 18 U.S.C. §§ 2 and 472. Smith moved to suppress the evidence that the officers discovered in the Camaro, arguing that the searches did not fall under either the search incident to an arrest exception or the automobile exception to the Fourth Amendment prohibition on warrantless searches. Initially, the district court agreed and granted Smith’s motion to suppress. Then the government moved for reconsideration, contending that no party had briefed the question of whether a search incident to an arrest could constitutionally precede the arrest. The district court granted the government’s motion for reconsideration.
After reconsidering, the district court held that (1) the search was valid as incident to the arrest because the officers had probable cause to arrest Smith before Officer Ratcliff searched the Camaro, and (2) Officer Ratcliff had probable cause to search the car under the automobile excep[948]*948tion. In so holding, the district court found that “this was a search incident to arrest, because it all happened at the same time”; “[t]he search started before the arrest, but it was completed ... after the arrest. By the time Officer [Ratcliff] started to search the car, they already knew Smith was lying. They already knew he had given false information. They could have arrested him right there.”
Smith entered a Stipulation and Conditional Plea Agreement with the government on November 6, 2003. Although Smith waived “any right to appeal or collaterally attack the conviction and sentence,” he retained the right to appeal the district court’s suppression ruling and any “sentence in excess of the high end of the guidelines range based on an adjusted offense level of 13.” During Smith’s plea colloquy, the district court explained this waiver to Smith and Smith indicated that he understood that by pleading guilty he would waive the right to appeal any sentence that did not exceed the high end of an offense level of 13.
On January 30, 2004, the district court sentenced Smith based on “a total adjusted offense level of 13,” and a criminal history category of IV. The corresponding guideline range for this combination is 24 to 30 months. The district court sentenced Smith in accordance with this range, “to custody for a period of 24 months.”
II. DISCUSSION
Smith raises several arguments on appeal. First, he claims that the district court’s dismissal of his motion to suppress was improper, given that the court had previously granted the motion. Second, Smith claims that the motion to suppress should have been granted because the evidence in question was the fruit of a war-rantless search, and did not fall under any recognized exception to the Fourth Amendment’s prohibition on warrantless searches and seizures. Finally, Smith challenges his sentence on the ground that the district court improperly used the “preponderance” rather than the “clear and convincing” evidentiary standard to apply a sentencing adjustment. We address each of these claims in turn.
A. The District Court’s Reconsideration of the Motion to Suppress
The district court did not err in reconsidering its initial grant of Smith’s motion to suppress. We have held that a district court may reconsider its prior rulings so long as it retains jurisdiction over the case. City of Los Angeles v. Santa Monica Baykeeper, 254 F.3d 882, 888 (9th Cir.2001). Because the district court never relinquished jurisdiction over Smith’s case, even after it granted his motion to suppress, the court retained the power to reconsider its own ruling.
“Under the ‘law of the case’ doctrine, a court is ordinarily precluded from reexamining an issue previously decided by the same court, or a higher court, in the same case.” Richardson v. United States, 841 F.2d 993, 996 (9th Cir.1988) (citations omitted). The doctrine is “a judicial invention designed to aid in the efficient operation of court affairs,” United States v. Lummi Indian Tribe, 235 F.3d 443, 452 (9th Cir.2000) (quoting Milgard Tempering, Inc. v. Selas Corp. of Am., 902 F.2d 703, 715 (9th Cir.1990)), and is “founded upon the sound public policy that litigation must come to an end,” Old Person v. Brown, 312 F.3d 1036, 1039 (9th Cir.2002), cert. denied, 540 U.S. 1016, 124 S.Ct. 566, 157 L.Ed.2d 429 (2003). Further, the doctrine serves to advance the “principle that in order to maintain consistency during the course of a single lawsuit, reconsideration of legal questions previously decided should be avoided.” United States v. [949]*949Houser, 804 F.2d 565, 567 (9th Cir.1986) (citation omitted). Notably, “[i]ssues that a district court determines during pretrial motions become law of the case.” United States v. Phillips, 367 F.3d 846, 856 (9th Cir.2004) (citation omitted) cert. denied, No. 04-5686, 125 S.Ct. 479, 2004 WL 2070630 (Nov. 8, 2004).
The law of the case doctrine is”not an inexorable command,” Hanna Boys Center v. Miller, 853 F.2d 682, 686 (9th Cir.1988) (citation omitted), nor is it “a limit to [a court’s] power.” Houser, 804 F.2d at 567-568. Rather, “[a]pplication of the doctrine is discretionary.” Lummi Indian Tribe, 235 F.3d at 452; see also Pickett v. Prince, 207 F.3d 402, 407 (7th Cir.2000) (stating that the “doctrine is highly flexible”) (citation omitted); Prisco v. A & D Carting Corp., 168 F.3d 593, 607 (2d Cir.1999); Avitia v. Metropolitan Club of Chicago, Inc., 49 F.3d 1219, 1227 (7th Cir.1995) (“A judge may reexamine his earlier ruling ... if he has a conviction at once strong and reasonable that the earlier ruling was wrong, and if rescinding it would not cause undue harm to the party that had benefitted from it.”) (citation omitted); Moore’s Federal Practice § 134.21[1] (3d ed. 2003) (“When a court applies the law of the case doctrine to its own prior decisions ... the traditional formulations of the doctrine must be conceived as rules of thumb and not as straightjackets on the informed discretion and sound practical judgment of the judge”).
The law of the case doctrine is “wholly inapposite” to circumstances where a district court seeks to reconsider an order over which it has not been divested of jurisdiction. See Santa Monica Baykeeper, 254 F.3d at 888. In Santa Monica Baykeeper, the district court sua sponte reconsidered its own order certifying for interlocutory appeal the denial of a motion to dismiss. Id. at 884. We were asked to assess whether the court’s reconsideration of its order violated the law of the case doctrine. Id. Our analysis emphasized the importance in law of the case doctrine jurisprudence of distinguishing between a district court’s consideration of its own prior decision and the directive of a higher court:
The legal effect of the doctrine of the law of the case depends upon whether the earlier ruling was made by a trial court or an appellate court. All rulings of a trial court are subject to revision at any time before the entry of judgment. A trial court may not, however, reconsider a question decided by an appellate court.
Id. at 888-89 (quoting, with emphasis added, Houser, 804 F.2d at 567). Accordingly, we determined that “[t]he doctrine simply does not impinge upon a district court’s power to reconsider its own interlocutory order provided that the district court has not been divested of jurisdiction over the order.” Id. at 888 (citing Houser, 804 F.2d at 567). Because the Baykeeper district court had rescinded its own prior order, over which it retained jurisdiction, we resolved that the court did not violate the law of the case doctrine. Id. at 889.
Just as in Santa Monica Baykeeper, the district court reconsidered its own order, over which its jurisdiction had not yet been divested. Therefore, under the authority of Santa Monica Baykeeper, the district court did not violate the law of the case doctrine. A survey of our sister circuits’ application of the law of the case doctrine provides additional support for this conclusion. See Avitia, 49 F.3d at 1227; Prisco, 168 F.3d at 607; see also Moore’s Federal Practice § 134.21[1] (3d ed.2003).
The cases upon which Smith relies to controvert this conclusion are inapplicable. In United States v. Alexander, 106 F.3d [950]*950874 (9th Cir.1997), we determined that the district court impermissibly departed from the law of the case doctrine by granting the government’s motion to reconsider the court’s previous order granting the defendant’s motion to suppress his confession. Id. at 875. Unlike in either Santa Monica Baykeeper or the case at hand, the district court in Alexander granted the motion to reconsider only “after the jury was unable to reach a verdict” and the court had declared a mistrial. Id. at 876 (emphasis added). By contrast, the district court here granted the motion in a timely manner. In Thomas v. Bible, 983 F.2d 152 (9th Cir.1993), the district court did not have jurisdiction to reconsider its prior order. In that case the district court’s reconsideration of a grant of attorney’s fees was improper because it was contrary to the appellate court’s determination that a party’s action was non-frivolous. See id. at 154-155. Because the appellate court’s determination was binding on the district court, that determination became the controlling law of the case, and the district court’s reconsideration was therefore improper. Unlike in Bible, the district court here retained jurisdiction over all issues in the case when it reconsidered its decision.
Because the district court retained jurisdiction when it reconsidered its prior grant of Smith’s motion to suppress, that reconsideration did not violate the law of the case doctrine and was not improper.
B. Defendant’s Motion to Suppress
We now turn to Smith’s appeal of the district court’s denial of his motion to suppress the evidence seized from his vehicle.1 The issues we confront are whether the officers had probable cause to arrest Smith, and, if they did, whether they could search, without a warrant, the passenger compartment of his car, and the containers found therein, when they had not placed Smith under arrest before the search occurred. We conclude that the search was a valid search incident to arrest because, at the time of the search, the officers had probable cause to arrest Smith, and the search was roughly contemporaneous with his arrest.
The district court’s conclusion that there was probable cause to arrest Smith at the time of the warrantless search, and that a search incident to arrest was permissible, present mixed questions of law and fact which we review de novo. United States v. Vasey, 834 F.2d 782, 785 (9th Cir.1987); United States v. Morgan, 799 F.2d 467, 468 (9th Cir.1986). We review for clear error the factual findings upon which the district court based its conclusions. United States v. Cunag, 371 F.3d 1060, 1063 (9th Cir.2004).
While the Fourth Amendment generally prohibits searches without a warrant, the warrant requirement is subject to some well-established exceptions. Flippo v. West Virginia, 528 U.S. 11, 13, 120 S.Ct. 7, 145 L.Ed.2d 16 (1999); Morgan v. United States, 323 F.3d 776, 781 (9th Cir.2003). Among these is the exception for a search incident to arrest. The search-incident-to-arrest exception permits law enforcement officers to conduct a warrantless search of a person who is arrested, and of his surrounding area, when the [951]*951search is incident to the arrest. Chimel v. California, 395 U.S. 752, 762-63, 89 S.Ct. 2034, 23 L.Ed.2d 685 (1969). Law enforcement officers may also search, contemporaneously with an arrest, the passenger compartment of an automobile and all containers found in the compartment. New York v. Belton, 453 U.S. 454, 460-61, 101 S.Ct. 2860, 69 L.Ed.2d 768 (1981). Such searches have long been considered valid, despite the absence of a warrant, because of the need to remove any weapons that threaten the arresting officers or bystanders and the need to prevent concealment or destruction of evidence. Chimel, 395 U.S. at 763, 89 S.Ct. 2034.
To ensure an appropriate balance between privacy and law enforcement interests, particularly in light of the prophylactic sweep of an automobile search incident to arrest, we have held that the critical inquiry in such cases is whether the search is “roughly contemporaneous with the arrest.” United States v. McLaughlin, 170 F.3d 889, 892 (9th Cir.1999). The requirement that the search and the arrest be roughly contemporaneous is not strictly temporal in nature. Rather, “[t]he relevant distinction turns not upon the moment of arrest versus the moment of the search but upon whether the arrest and search are so separated in time or by intervening acts that the latter cannot be said to have been incident to the former.” Id. at 893 (quoting United States v. Abdul-Saboor, 85 F.3d 664, 668 (D.C.Cir.1996)).
Applying the requirement that a search be contemporaneous with an arrest, we have held that a search need not be conducted immediately upon the heels of an arrest, but sometimes may be conducted well after the arrest, so long as it occurs during a continuous sequence of events. Thus in McLaughlin, we held that the search of a defendant’s car conducted five minutes after the arresting officer drove the defendant from the scene was a valid search incident to arrest because the arrest, the completion of required paperwork, and the initial search were all “one continuous series of events closely connected in time.” McLaughlin, 170 F.3d at 893. Similarly, in United States v. Hudson, 100 F.3d 1409 (9th Cir.1996), we held that a search of the defendant’s bedroom, conducted about three minutes after the defendant had been arrested, handcuffed, and removed from the house was a valid search incident to arrest. Id. at 1413, 1419. Again, our focus was not strictly on the timing of the search but its relationship to (and reasonableness in light of) the circumstances of the arrest. See id.
A search incident to arrest need not be delayed until the arrest is effected. Rather, when an arrest follows “quickly on the heels” of the search, it is not particularly important that the search preceded the arrest rather than vice versa. Rawlings v. Kentucky, 448 U.S. 98, 111, 100 S.Ct. 2556, 65 L.Ed.2d 633 (1980). So long as an arrest that follows a search is supported by probable cause independent of the fruits of the search, the precise timing of the search is not critical. Id.; United States v. Morgan, 799 F.2d 467, 469 (9th Cir.1986); see also United States v. Potter, 895 F.2d 1231, 1234 (9th Cir.1990) (finding no Fourth Amendment violation for pre-arrest “pat down” search of suspect based on probable cause to arrest, and noting that “[a] search incident to an arrest is valid whether it occurs immediately before or after the arrest.”); United States v. Salazar, 805 F.2d 1394, 1399 (9th Cir.1986) (stating, in dicta, “it is not particularly important in this case that the formal arrest followed rather than preceded the search, for the search is still valid as incident to the lawful arrest if it did not exceed the scope of the exception.”), over[952]*952ruled on other grounds by California v. Acevedo, 500 U.S. 565, 111 S.Ct. 1982, 114 L.Ed.2d 619 (1991).
We have held that the warrantless search of a person incident to a contemporaneous arrest may precede the arrest, but we have not heretofore specifically held that the warrantless search of a vehicle incident to a contemporaneous arrest may precede the arrest. There is, however, no sound reason to treat these circumstances differently.2 See Thornton v. United States, 541 U.S. 615, -, -, 124 S.Ct. 2127, 2131, 2132, 158 L.Ed.2d 905 (2004) (suggesting that because of the need for clear rules and in light of the danger and fluidity of arrests, “[o]nce an officer determines that there is probable cause to make an arrest, it is reasonable to allow officers to ensure their safety and to preserve evidence by searching the entire passenger compartment.”); Salazar, 805 F.2d at 1399 (“The police, after removing the occupants of the car, searched the car and the closed bag on the rear floor-board. That search comes within the permissible boundaries of the ‘incident to arrest’ exception established by the Supreme Court in New York v. Belton”); United States v. Lugo, 170 F.3d 996 (10th Cir.1999) (holding that search of vehicle before arrest is valid “so long as: (1) there existed a legitimate basis for the arrest before the search; and (2) the arrest took place shortly after the search.”). Accordingly, we now hold that as long as there is probable cause to make an arrest, and the search is conducted roughly contemporaneously with the arrest, the search-ineident-to-arrest doctrine applies and no warrant is required.
Each of the requirements for a valid search incident to arrest is satisfied in the present case. There was probable cause to make the arrest immediately preceding the search. Not only did Smith fail to provide a driver’s license to validate his identity, the identity information he did provide failed to match any driver’s license record in California or Arizona. Further investigation turned up a match to an Arizona driver’s license listing the name, address, and social security number provided by Smith, but that listing contained a date of birth one year off from the date Smith had given. More importantly, the record investigated revealed a physical description for Vernon Smith, the name the defendant Kory Smith provided as his own, that was substantially different from Kory Smith’s physical characteristics. At this point, it became clear to the officers that Kory Smith had falsely represented his identity. In these circumstances, the officers had probable cause to believe that Smith had committed a crime, see Potter, 895 F.2d at 1233-34, and they had probable cause to arrest him.
The arrest followed the search of Smith’s car, but probable cause for the arrest preceded the search. There was no significant delay in the series of events [953]*953from the moment probable cause arose, to the initial search of Smith’s car, to his arrest. Thus, the search of Smith’s car was A “contemporaneous incident of [a lawful] arrest.” Belton, 453 U.S. at 460, 101 S.Ct. 2860. We conclude that the district court did not err in denying Smith’s motion to suppress.
C. Smith’s Right to Appeal His Sentence
Smith argues that the district court erred in applying the preponderance of evidence rather than the clear and convincing evidentiary standard, when it adjusted Smith’s sentence up six levels. Because Smith waived “any right to appeal or collaterally attack the conviction and sentence,” we do not reach this question.
We review de novo the question of whether an appellant has waived his right to appeal. United States v. Shimoda, 334 F.3d 846, 848 (9th Cir.2003). “Generally, courts will enforce a defendant’s waiver of his right to appeal if (1) the language of the waiver encompasses the defendant’s right to appeal on the grounds claimed on appeal, and (2) the waiver is ‘knowingly and voluntarily made.’ ” United States v. Martinez, 143 F.3d 1266, 1270-71 (9th Cir.1998) (citations and quotation omitted).
“Pursuant to the first requirement, we determine whether the agreement, by its terms, waives the right to appeal.” United States v. Nunez, 223 F.3d 956, 958 (9th Cir.2000). In the plea agreement Smith formed with the government, Smith waived “any right to appeal or collaterally attack the conviction and sentence,” unless the “sentence [exceeded] the high end of the guideline range based on an adjusted offense level of 13.” The district court sentenced Smith, based on “a total adjusted offense level of 13” and a criminal history category of IV, “to custody for a period of 24 months.” Because the guideline range for an offense level of 13 and a criminal history category of IV is 24 to 30 months, the district court’s sentence fell within the range for which Smith waived his right to appeal. “The second requirement for a valid waiver is that the defendant knowingly and voluntarily consent to the agreement’s express terms.” Id.; (citing Fed.R.Crim.P. 11(c) & (d)). The record clearly shows that Smith’s waiver of his appellate rights was knowing and voluntary. Therefore, our “inquiry into the waiver’s validity is at an end; the valid waiver bars [Smith’s] ... challenges to his ... sentence and we must dismiss the appeal.” United States v. Nguyen, 235 F.3d 1179, 1182 (9th Cir.2000) (citing United States v. Michlin, 34 F.3d 896, 898 (9th Cir.1994)).
III. CONCLUSION
For the foregoing reasons, Smith’s conviction is AFFIRMED and the appeal to his sentence is DISMISSED.